Buckling and vibration analysis nanoplates with imperfections

In the present paper a coupling finite strip–finite element procedure is developed to investigate the buckling and vibration behaviour of imperfect nanoplates via nonlocal Mindlin plate theory. The imperfection can be either a thickness variation or a lack of planarity and it can be either localized or distributed on an entire edge of the nanoplate. The resulting nonlinear equations are solved exactly by applying the Kantorovich method. A finite element approach is proposed for coupling the in-plane and the out-of-plane buckling equations to describe properly the imperfections. Some numerical examples are carried out in order to show the sensitivity of the results to the nonlocal parameter and to the imperfection.